Quantum Chemistry 3.3 – Eigenvalues and Eigenfunctions

Short lecture on eigenvalues and eigenfunctions.

When the result of an operator acting on a function is a constant multiplied by the same function, the function is called an eigenfunction, and the constant is called an eigenvalue. The eigenvalue problem is to determine the set of eigenfunctions and eigenvalues for a given operator. The Schrodinger equation is an eigenvalue problem for the Hamiltonian operator, where the wavefunction is the eigenfunction and the eigenvalue is the total energy of the state. Eigenvalue equations could be solved in quantum mechanics for any operator, including kinetic energy, potential energy, momentum, and position.

Notes Slide: http://i.imgur.com/4AWkJJm.png

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